On the automorphism groups of almost all circulant graphs and digraphs

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dc.contributor.authorBhoumik, Soumya
dc.contributor.authorDobson, Edward
dc.contributor.authorMorris, Joy
dc.date.accessioned2018-07-10T17:57:48Z
dc.date.available2018-07-10T17:57:48Z
dc.date.issued2018
dc.descriptionOpen access, licensed under Creative Commonsen_US
dc.description.abstractWe attempt to determine the structure of the automorphism group of a generic circulant graph. We first show that almost all circulant graphs have automorphism groups as small as possible. The second author has conjectured that almost all of the remaining circulant (di)graphs (those whose automorphism group is not as small as possible) are normal circulant (di)graphs. We show this conjecture is not true in general, but is true if we consider only those circulant (di)graphs whose order is in a “large” subset of integers. We note that all non-normal circulant (di)graphs can be classified into two natural classes (generalized wreath products, and deleted wreath type), and show that neither of these classes contains almost every non-normal circulant digraph.en_US
dc.description.peer-reviewYesen_US
dc.identifier.citationBhoumik, S., Dobson, E., & Morris, J. (2014). On the automorphism of almost all circulant graphs and digraphs. Ars Mathematica Contemporanea, 7(2), 487-506en_US
dc.identifier.urihttps://hdl.handle.net/10133/5162
dc.language.isoen_USen_US
dc.publisherDrustvo Matematikov, Fizikov in Astronomoven_US
dc.publisher.departmentDepartment of Mathematics and Computer Scienceen_US
dc.publisher.facultyArts and Scienceen_US
dc.publisher.institutionFort Hays State Universityen_US
dc.publisher.institutionMississippi State Universityen_US
dc.publisher.institutionUniversity of Primorskaen_US
dc.publisher.institutionUniversity of Lethbridgeen_US
dc.subjectCirculant graphen_US
dc.subjectAutomorphism groupen_US
dc.subjectCaley graphen_US
dc.subjectDRRen_US
dc.subjectGRRen_US
dc.subjectDigraphs
dc.subject.lcshAutomorphisms
dc.subject.lcshCaley graphs
dc.subject.lcshGraph theory
dc.titleOn the automorphism groups of almost all circulant graphs and digraphsen_US
dc.typeArticleen_US
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